In this paper we are concerned with the distribution of observed or reported incomes in the context of a model that assumes underreporting. A form of `errors-in-variables' model is considered and the Pareto distribution is shown to exhibit certain invariance properties. Under this model (a) the distribution of observed incomes suitably truncated coincides with the true distribution if and only if the distribution is of the Pareto form and (b) a variable having a linear regression on true income has a linear regression on observed income also if and only if the distribution is of the Pareto type.